Number Theory and the Periodicity of Matter

1. Front Matter

   Pages i-xv

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2. Introduction

   Pages 1-17

3. Number Theory Primer

   Pages 19-69

4. Periodic Table of the Elements

   Pages 71-129

5. Structure of Atomic Nuclei

   Pages 131-181

6. Elements of Cosmography

   Pages 183-208

7. The Periodic Laws

   Pages 209-236

8. Periodicity and Number Theory

   Pages 237-257

9. Properties of Atomic Matter

   Pages 259-290

10. The Grand Pattern

    Pages 291-301

11. The Golden Excess

    Pages 303-334

12. Chemical Periodicity

    Pages 335-355

13. Back Matter

    Pages 357-374

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Of all the great innovations and intellectual achievements of mankind there is nothing that rivals the invention of counting and discovery of the number system. The way in which this discovery led to the development of abstract higher mathematics is the least of its merits, compared to the universal f- cination that the natural numbers hold for all people. Numbers are at the roots of magic, superstition, religion and science. Numerologists can int- pret great historical and cosmicevents, predict thefuture and explain human nature. Better informed, sophisticated people may frown upon and ridicule such claims,but the number of incidents that link numbers tophysical e?ects is simply too large to ignore as mere coincidence. It is in cases like these that the more respectable number theory is substituted for numerology. Although it is recognized as the most fundamental branch of mathem- ics,thevocabulary ofnumbertheoryincludesconcepts suchasprimenumber, perfect number, amicable number, square number, triangular number, py- midal number, and even magic number, none of which sounds too scienti?c and may suggest a di?erent status for the subject. Not surprisingly, number theory remains the pastime of amateurs and professionals alike – all the way from the great Gauss down. It may be claimed that abstract number theory is more lofty than mundane science, never to be degraded into a servant of physical theory.

• Arithmetic
• Fibonacci phylotaxis
• crystallographic periodicity
• function
• golden ratio
• hidden symmetry
• number patterns
• periodic structures
• physical systems

From the reviews:

"The book launch was held at the University of Pretoria (UP) on 26 March 2008. … It’s a fascinating and original concept and I hope you all get the opportunity to read it. It will challenge your current views of numbers. … If there is a link between numbers and the Periodic Table this will of course have major implications as to the ‘meaning’ on the Periodic Table. It’s great to have original thinkers in our midst!" (South African Chemical Institute Newsletter, Issue 3, 2008)

"Some people believe that there exist links between the natural numbers and the physical world. This … book looks for such links in what the authors call ‘the periodicity of matter.’ Readers with an interest in mathematics, science, or natural philosophy will find the book useful … . it is aimed at researchers working on various branches of physics who might find it interesting to find related ideas in number theory. … can be of interest to mathematicians, physicists and chemists." (Soheila Emamyari and Mehdi Hassani, MathDL, May, 2008)

"This remarkable book will be found interesting by scholars whose expertise lies in one or more of the following disciplines: philosophy, applied mathematics, theoretical, nuclear, and elementary particle physics, as well as physical, theoretical, and mathematical chemistry. … the book Number Theory and the Periodicity of Matter is an exciting and nonstandard feat in the study of Nature. … is recommended to the readers of MATCH Communications in Mathematical and in Computer Chemistry. Yet, its the main readers should be nuclear physicists." (Ivan Gutman, MATCH Communications in Mathematical and in Computer Chemistry, Vol. 60, 2008)

"The authors discuss connections between number and matter and write about primes and the golden ratio somehow underlying nuclear physics. This book learnedly summarizes much scientific knowledge and history (mathematics, chemical physics, nuclearphysics, cosmology), and may thus serve some readers independently of its main project. Summing Up: Recommended. Upper-division undergraduates and up." (D. V. Feldman, Choice, Vol. 46 (2), October, 2008)

"This is a book of special interest for particle physicists and chemists. … this is a recommendable and interesting book." (H. Zimmermann, Crystallography Reviews, May, 2009)

"The current volume has been written for readers at diverse levels of scientific and mathematical education as well as an exceptionally wide range of interests in natural phenomena. … the current book a valuable contribution to one’s library." (Joel F. Liebman, Molecular Crystals and Liquid Crystals, Vol. 503, June, 2009)

• University of Pretoria, South Africa

  Jan C. A. Boeyens

• University of the Witwatersrand, South Africa

  Demetrius C. Levendis

Policies and ethics